Question

Hi, can anyone help me on this question :
Show that a positive logic AND gate is a negative logic OR gate and vice versa.

Answer 1

If you write out truth table for each one of them, would that be sufficient of a proof?

Answer 2

yes

Answer 3

it will be best if you can elaborate the answer so that i can understand :) @c0decracker

Answer 4

These are the basics of truth tables:
http://www.sparknotes.com/math/geometry3/logicstatements/section4.rhtml

College examples:
http://www.math.csusb.edu/notes/logic/lognot/node1.html
http://www.millersville.edu/~bikenaga/math-proof/truth-tables/truth-tables.html

And what Wikipedia ahs on this:
http://en.wikipedia.org/wiki/Truth_table

Basically you make a table and show the conditions and results. So when X is this and Y is that, this is the result.

\(
\begin{array}{|c|c|c|}\hline
x & y & x \;\&\; y \\ \hline
\text{T} & \text{T} & \text{T} \\ \hline
\text{T} & \text{F} & \text{F} \\ \hline
\end{array}
\)

And so on.

See, in that case, when X and Y are both true, X&Y is also true. When only one is true, the result is false. You build a table like that, but with two result columns. One result column is the AND the other is the NOR. If both the AND and NOR columns match, you have proven the hypotheses that they are logical equivalents.

Answer 5

I have to also add that this is a cool example in CS of a mathematical principle in set theory called DeMorgan's law

Answer 6

?

Answer 7

? What